Q. 164.8( 12 Votes )

# The area of circular field is 154 sq cm. Let us write by calculating the perimeter and area of circumference circular field with square.

Answer :

Given: Area of circle = 154 cm^{2}

We know that

Area of a circle = πr^{2}

⇒ πr^{2} = 154

⇒ r^{2} = 7× 7

⇒ r = 7 cm

Also, Diameter of the circle = 2× radius

⇒ CE = 2× 7 = 14 cm

This acts as the diagonal of the inscribed square.

So, the diagonal of the square BCDE= 14 cm

Let the side of the square be x cm

We know that each angle of a square is 90°.

Using Pythagoras theorem,

CD^{2} +DE^{2} = CE^{2}

⇒x^{2}+ x^{2} = 14^{2}

⇒ 2x^{2} = 196

⇒x^{2} =98

Side of the square =7√2 cm

We know that Area of a Square = side× side

⇒ Area of BCDE =98 cm^{2}

Perimeter of a square = 4× side

⇒ Perimeter of BCDE = 4× 7√2 = 28√2 cm

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